plz help - algebraic problem...who can solve?

Question

A 120 page book has 'p' lines to a page. If the number of lines were reduced by three on each page the number of pages would need to be increase by 20 to give the same amount of writing space. How many lines were there on the page originally?

Could you plz explain how you got the answer? Thanks a lot

Answer 1

120 times p = lines in a book
(120 + 20 ) times p-3 = same number of lines

so 120p = 140p - 420
subtract 420 each side
120p + 420 = 140p
subtract 120p each side
420 = 20p
p = 21

original number of lines per page is 21

21 x 120 = 2520
18 x 140 = 2520

tada!!!!!!!!!!!!!!!!!

Answer 2

Hi MS,

If at the start we have 120 pages, and 'p' lines in each page, we have a total of
120*p lines

Now, if the number of lines are reduced by three on each page the number of pages would need to be increase by 20 to give the
same amount of writing space. So, the new number of pages is 140 (120 + 20).
Since the writing space is same, so
120*p = 140 * (p-3)
120*p = 140*p - 420
420 = 140*p - 120*p = 20*p

So,
420=20*p
p=21

So, there were 21 lines on the page originally.

Answer 3

120 p = x = 140 (p- 3), solve for p, 20 p - 420 = 0, p = 21.

Explanation let x equal the total number of lines, Known 120 * p = X
120 + 20 = 140 pages in new layout. 140* l = X and l = p-3. follow the algbra above

Answer 4

how you doin' MS?
if at the start we have 120 pages, and 'p' lines in each page, we have a total of 120*p lines. right?
now, they tell us that if each page had (p-3) lines, we had to add 20 pages (120+20 = total 140 pages) to get the same number of lines alltogether. we have an equation:

120*p = 140 * (p-3)

we open the parenthesis (???)

120*p = 140*p - 420

we move 120*p to the right side with a minus sign, and move 420 to the left side with a positive sign. we get

420 = 140*p - 120*p = 20*p

we divided both sides of the equation by 20, getting

420 / 20 = 21 = p

that means that originally, each page had 21 lines. got it?

Answer 5

p*120=140*(p-3)=140*p-420

20*p=420

p = 420/20 = 21 lines on the original page.

Answer 6

120p=140(p-3)
20p=420
p=21